Between 2000 and 2005, the quantity of automobiles produced and sold declined by

Question

Between 2000 and 2005, the quantity of automobiles produced and sold declined by 20%. During this period the real price of cars increased by 5%, real income levels declined by 2%, and the real cost of gasoline increased by 20%. Knowing that the income elasticity of demand is +1.5 and the cross price elasticity of gasoline and cars is -0.3

Compute the price elasticity of the demand for the cars during this period.

So the answer gives me ED as -2.2.
-20% = 1.5(-2%) + (-0.3)(20%) + (ED)(5%)
ED = -2.2

It's been a while since I've taken algebra and I think the reason the answer is 2.2 is because we move the (ED)(5%) to the left hand side of the equation and the -20% to the right...

ED(5%) = 20% + (-3%) + (-6%)
ED(5%) = -11% / 5 = -2.2

Am I doing this correctly? Does the -20% that we move from the left to the right become positive when we move it to the right? If not, can you break it down how we got the ED = -2.2?

Thanks in advance.

Explanation / Answer

So the answer gives me ED as -2.2. -20% = 1.5(-2%) + (-0.3)(20%) + (ED)(5%) ED = -2.2 Your formula is correct this time...let me see if I can walk you through the algebra. Start by converting percentages to decimals. -.2=-.02(1.5)+.2(-.3)+.05(ED) Now, I will multiply the first two terms: -.2=(-.03)+(-.06)+.05(ED) Add the first two terms: -.2=(-.09)+.05(ED) Add .09 to both sides: -.11=.05(ED) Divide both sides by .05 -2.2=ED Hopefully, this clears up any confusion. Let me know if you have other questions.

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